
if we can bound \(||(\Sigma _{\mathcal {Z}}^*+u\Delta _{\mathcal {Z}})^{-1}-\Omega _{\mathcal {Z}}^*||_{\infty }\)  and \(||(\Sigma _{\mathcal {Z}}^*+u\Delta _{\mathcal {Z}})^{-1}{\bf S}(\Sigma _{\mathcal {Z}}^*+u\Delta _{\mathcal {Z}})^{-1}-{\bf U}_{\mathcal {Z}}||_{\infty }\)  by some polynomial with respect to \(||\Delta _{\mathcal {Z}}||_{\operatorname{F}}\)  with probability tending to one as in the proof of Lemma 4.3 in [1]}, we can establish Lemma REF . Using the similar argument in (A.17)-(A.18) of [1]}, it can be shown that
\(||(\Sigma _{\mathcal {Z}}^*+u\Delta _{\mathcal {Z}})^{-1}-\Sigma _{\mathcal {Z}}^*||_{\infty }&\le K||\Delta _{\mathcal {Z}}||_{\operatorname{F}}\) 
